The governor graduated from Brown in 1975 and one of his children is a student there now. He convened the 1 p.m. meeting in his State House office because he “believes in collaboration and believes we all have to work together to solve our city’s and state’s problems,” Chafee spokeswoman Christine Hunsinger said.

“I’d characterize the meeting as going well,” she added.

Taveras and Simmons have been at loggerheads since December, when negotiations over Brown’s voluntary payments to the city broke down after the university’s board rejected the mayor’s request for $4 million in additional annual payments and he spurned their counteroffer of $2 million.

“Brown supports Providence, and we have offered to do more during this particularly challenging time,” Quinn said, noting the city’s four private schools already plan to pay $50 million over 20 years. “We regret that the mayor rejected this offer, and hope we can continue our discussions and reach an equitable, sustainable solution.”

Taveras warned earlier Thursday that Providence is “on the brink of bankruptcy” and asked for “shared sacrifices” from city retirees and tax-exempt institutions like Brown and the hospitals. The mayor is scheduled to meet with Central Falls receiver Robert Flanders on Friday.

Walt Buteau contributed to this report. This post has been updated and expanded. An earlier version incorrectly said Brown has agreed to pay $50 million to the city over 20 years; that will be paid by all four private schools, including Brown.